Fast MCMC sampling for hidden markov models to determine copy number variations

Abstract

BackgroundHidden Markov Models (HMM) are often used for analyzing Comparative Genomic Hybridization (CGH) data to identify chromosomal aberrations or copy number variations by segmenting observation sequences. For efficiency reasons the parameters of a HMM are often estimated with maximum likelihood and a segmentation is obtained with the Viterbi algorithm. This introduces considerable uncertainty in the segmentation, which can be avoided with Bayesian approaches integrating out parameters using Markov Chain Monte Carlo (MCMC) sampling. While the advantages of Bayesian approaches have been clearly demonstrated, the likelihood based approaches are still preferred in practice for their lower running times; datasets coming from high-density arrays and next generation sequencing amplify these problems.ResultsWe propose an approximate sampling technique, inspired by compression of discrete sequences in HMM computations and by kd-trees to leverage spatial relations between data points in typical data sets, to speed up the MCMC sampling.ConclusionsWe test our approximate sampling method on simulated and biological ArrayCGH datasets and high-density SNP arrays, and demonstrate a speed-up of 10 to 60 respectively 90 while achieving competitive results with the state-of-the art Bayesian approaches.Availability: An implementation of our method will be made available as part of the open source GHMM library from http://ghmm.org.

Fast detection of de novo copy number variants from SNP arrays for case-parent trios

“…Similarly, HMM algorithms were originally formulated for aCGH platforms [22] and many innovations were subsequently proposed. For example, distance-based transition probabilities [6], fully Bayesian HMMs [23], reversible jump and approximate sampling Markov chain Monte Carlo (MCMC) [24,25], iterative approaches to parameter estimation [26], alternatives to the Viterbi algorithm [27], and higher order Markov chains [28]. As HMMs readily accomodate multiple data sequences, the observation that copy number can be estimated from genotyping arrays [29] led to the development of several HMMs that jointly model copy number and genotypes at SNPs [30-37].…”

Fast Bayesian Inference of Copy Number Variants using Hidden Markov Models with Wavelet Compression

“…Following [62], we report F-measures (F 1 scores) for binary classification into normal and aberrant segments ( Fig. 2), using the usual definition of F = 2πρ π+ρ being the harmonic mean of precision π = TP TP+FP and recall ρ = TP TP+FN , where TP, FP, TN and FN denote true/false positives/negatives, respectively.…”

“…Though there are several schemes available to sample q, [58] has argued strongly in favor of Forward-Backward sampling [57], which yields Forward-Backward Gibbs sampling (FBG) above. Variations of this have been implemented for segmentation of aCGH data before [60,62,78]. However, since in each iteration a quadratic number of terms has to be calculated at each position to obtain the forward variables, and a state has to be sampled at each position in the backward step, this method is still expensive for large data.…”

“…However, since in each iteration a quadratic number of terms has to be calculated at each position to obtain the forward variables, and a state has to be sampled at each position in the backward step, this method is still expensive for large data. Recently, [62] have introduced compressed FBG by sampling over a shorter sequence of sufficient statistics of data segments which are likely to come from the same underlying state. Let B := (B w ) W w=1 be a partition of y into W blocks.…”

Dynamic expression of 3′ UTRs revealed by Poisson hidden Markov modeling of RNA-Seq: Implications in gene expression profiling

“…Our approach uses a Poisson hidden Markov model (PHMM) to 1) estimate (hidden) states of gene expression levels in terminal exon 3′ UTRs, 2) infer shortening of the region in human liver and brain cortex tissues and 3) demonstrate tissue-specific APA. Others have used hidden Markov models (HMMs) in a similar fashion to dynamically map chromatin states (Ernst et al, 2011), to integrate genomic data (Day et al, 2007) and for determination of gene copy number variations (Mahmud and Schliep, 2011) just to name a few. We compare our results to those obtained by MISO, a probabilistic approach to quantification of transcripts at the 3′ UTR (Katz et al, 2010) and Cufflinks, based on de novo transcript assembly (Trapnell et al, 2010).…”